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Image Deblurring and Denoising using Color Priors

Image Deblurring and Denoising using Color Priors. Neel Joshiy , C. Lawrence Zitnicky , Richard Szeliskiy , David J. Kriegman Microsoft Research University of California, San Diego. Outline. Introduction Deconvolution and Denoising Overview Gradient Priors Color Priors

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Image Deblurring and Denoising using Color Priors

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  1. Image Deblurring and Denoising using Color Priors Neel Joshiy, C. Lawrence Zitnicky, Richard Szeliskiy, David J. Kriegman Microsoft Research University of California, San Diego

  2. Outline • Introduction • Deconvolution and Denoising Overview • Gradient Priors • Color Priors • Recovering the Sharp Image • Results • Conclusion

  3. Introduction • They propose using priors derived from image color statistics for deconvolution and denoising. • Their prior models an image as a per-pixel linear combination of two color layers, where the layer colors are expected to vary more slowly than the image itself. • Our approach places priors on the values used for blending between the two colors, in essence creating a robust edge prior that is independent of gradient magnitude.

  4. Introduction • Denoisingcan be considered a subproblem of deblurring. • Deconvolutionmethods can be used purely for denoising by considering the blurring kernel to be a delta function. • Thus, they treat denoising as a subproblem of deconvolution and present a non-blind deconvolution algorithm that can be used for both applications.

  5. Deconvolution and Denoising Overview • They model a blurred, noisy image as the convolution of a latent sharp image with a known shift-invariant kernel plus additive white Gaussian noise

  6. Gradient Priors • The role of the image prioris to disambiguate among the set of possible solutions andto reduce over-fitting to the noise. • These interactions can be modeledusing a Markov Random Field (MRF) in which the value ofan individual pixel is conditionally dependent on the pixelvalues in a local neighborhood. • Typically, this is enforcedunder a assumption of a Gaussian distribution on theimage gradients.

  7. Gradient Priors • Deconvolution using a sparse gradient prior is a significantstep towards producing more pleasing results, as itreduces ringing artifacts and noise relative to more traditionaltechniques. • Two limitation: 1.Finding the lowest intensity edges that are consistent with the observed blurred image. 2. This can result in the preservation and sharpening of the noise.

  8. Gradient Priors

  9. Color Priors • The TwoColor Model • Two benefits: 1.Given the two colors for a pixel, the space of unknowns is reduced from three dimensions (RGB) to one ( ). 2. The parameter provides an alternative for parameterizing edges, where the edge sharpness is decoupled from edge intensity—a single pixel transition in from 1 to 0 indicates a step edge (an single step from primary to secondary) regardless of the intensity of the edge.

  10. Color Priors • Their two-color model is a Gaussian Mixture Model that is a modified version of the approach used by Bennett et al. • After several iterations the Gaussians will merge if the standard deviation is less than the noise’s standard deviation.

  11. Color Priors • Using the TwoColor Model for Deconvolution • The first is to use the model as a hard constraint, where the sharp image I must always be a linear combination of the primary and secondary colors P and S. • The second is to use a soft-constraint to encourage I to lie on the line connecting P and S in RGB space.

  12. Color Priors

  13. Recovering the Sharp Image • The full definition of our model has two minima in the penalty function—one at 0 and the other at 1. • The only way to properly minimize this exact error function is using a costly non-linear optimization. • Given a few observations about our error function and one approximation, we can use a much faster iterative-leastsquares (IRLS) approach.

  14. Recovering the Sharp Image • As in the Levin et al.’s work, we minimize the hyper-Laplacian prior using a re-weighting function.

  15. Results

  16. Results

  17. Conclusion • The first being to investigate alternative optimization techniques. • The second is to improve the initialization for the color model. • They found that using the sparse prior alone with a low weighting provides a good initial guess. • Due to our current optimization method, the quality of our results is somewhat bound by this initialization.

  18. Conclusion • They have found that varying the weighting of the alpha priors can help create better results. • We are interested in exploring the alpha prior and weighting values in a class-specific way. • We believe that there may be a consistent, but different, set of weights for text versus natural images.

  19. ENDThanks for listening

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